Effect of streamflow forecast uncertainty on real-time reservoir operation

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Abstract

Various hydrological forecast products have been applied to real-time reservoir operation, including deterministic streamflow forecast (DSF), DSF-based probabilistic streamflow forecast (pseudo-PSF, pPSF), and ensemble or probabilistic streamflow forecast (denoted as real-PSF, rPSF). DSF represents forecast uncertainty in the form of deterministic forecast errors, pPSF a conditional distribution of forecast uncertainty for a given DSF, and rPSF a probabilistic uncertainty distribution. Compared to previous studies that treat the forecast products as ad hoc inputs for reservoir operation models, this paper attempts to model the dynamic evolution of uncertainties involved in the various forecast products and explores their effect on real-time reservoir operation decisions. Through a hypothetical example of a single-objective real-time reservoir operation model, the results illustrate that forecast uncertainty exerts significant effects. Reservoir operation efficiency, as measured by a utility function, decreases as the forecast uncertainty increases but the magnitude depends on the forecast products used. In general, the utility of the reservoir operation with rPSF is nearly as high as the utility obtained with a perfect forecast. Meanwhile, the utilities of DSF and pPSF are similar to each other but not as high as rPSF. Moreover, streamflow variability and reservoir capacity can change the magnitude of the effects of forecast uncertainty, but not the relative merit of DSF, pPSF, and rPSF.

Research highlights

► A dynamic uncertainty evolution model is used to characterize streamflow forecast. ► Modeled forecast uncertainty is incorporated to dynamic reservoir operation. ► Ensemble and probabilistic forecasts have high potential for improving decisions.

Introduction

Advances in weather forecasting, hydrologic modeling, and hydro-climatic teleconnection relationships have significantly improved streamflow forecast precision and lead-time [3], [22], [24], [28] and provide great opportunities to improve the efficiency of water resources system operations [23], [25], [29], [39]. In recent years, forecast products, particularly long-term streamflow forecasts (with a lead-time longer than 15 days), have been applied to reservoir operation and water resources management (e.g. [23], [25], [29], [39]).

In addition to forecast precision and lead-time, operation strategies also influence the efficiency of utilizing streamflow forecasts for real-time reservoir operation [4], [20], [39]. As a common practice, reservoir operation curves, which set a target storage level for each operation period around a year, are adopted as guidelines for real-time reservoir operation as well as for operation planning [18], [34]. Since operation curves are determined by historical streamflow records [20], [34], they reflect suitable reservoir operation decisions under various historical scenarios rather than real-time streamflow conditions. Thus, even a perfect streamflow forecast cannot improve reservoir operation efficiency when operation curves are used [39]. In many recent studies, reservoir operation curves have been replaced by real-time reservoir optimization and simulation models, which are supposed to provide more flexible and efficient approaches utilizing various streamflow forecast products [8].

One important issue with implementing streamflow forecasts in real-time reservoir operation models is dealing with the uncertainty involved in streamflow forecast products [8], [9], [26]. Although forecast uncertainty analysis has been one research focus in hydrology (e.g. [17], [31], [32]), there are comparatively less studies on the effect of forecast uncertainty on real-time reservoir operations [9], [27], [33]. Deterministic or probabilistic streamflow forecast products are usually treated as ad hoc inputs for deterministic or stochastic reservoir operation models. That is to say, a deterministic forecast or a stochastic forecast represented by a number of scenarios is pre-designed for a specific reservoir operation problem for screening test, and no non-generalizable structure of the forecast error is endogenously involved in the operation analysis. Correspondingly, many previous studies on forecast and reservoir operation in the literature adopt a two-component approach, one provides (“recommends”) a forecast scenario [3], [22], [24], [28] as input to the other component [23], [25], [29], [39] that dealing with forecast application. In general, such an approach suggests that forecast can always improve reservoir operation efficiency especially under extreme conditions [21].

This study aims at analyzing the effect of forecast uncertainty on real-time reservoir operations. As different forecast products, e.g., deterministic and probabilistic streamflow forecasts, can exert different effects on real-time reservoir operation decisions in optimization and simulation models, this study will explicitly simulate the uncertainty in each of the streamflow forecasts examined and assess its effect on real-time reservoir operation decisions. Since the tool for such a purpose does not exist in the hydrologic literature, the Martingale Model of Forecasting Evolution (MMFE) [11], [12] used in supply chain management is introduced to quantify real-time streamflow forecast uncertainty and generate deterministic and probabilistic forecast products. Simulations based on standard operation policy (SOP), dynamic programming (DP), and stochastic dynamic programming (SDP) [16], [18] are adopted to determine release decisions for a hypothetical reservoir using synthetic streamflow forecasting products.

The rest of the paper is organized as follows. Section 2 provides some background information on streamflow forecasting and forecast uncertainty and introduces the Martingale Model of Forecasting Evolution (MMFE). Section 3 describes the MMFE-based forecast uncertainty analysis in real-time reservoir operation. Section 4 introduces the numerical experiments designed in this study. Section 5 analyzes the results and Section 6 contains the conclusions.

Section snippets

Background

In hydrology, there are various indices reflecting the magnitude of streamflow forecast uncertainty (e.g., [24], [32]). However, few models illustrate the forecast uncertainty evolution process. This paper adopts MMFE from supply chain management [11], [12] to quantify the evolution of the uncertainty of real-time streamflow forecasts as time progresses.

MMFE-based streamflow forecast uncertainty analysis

To use MMFE to model the uncertainty of streamflow forecasts, it is necessary to justify its assumptions, i.e. unbiasedness, non inter-period correlation, stationarity, and Gaussian distribution. Real-time streamflow forecasts are based on hydrologic model inputs, such as precipitation, temperature, and soil moisture. These inputs are updated at the beginning of each period with new weather forecasts and hydrologic observations (e.g., streamflow, soil moisture) to improve the preceding

Numerical experiments

A hypothetical reservoir system with N operation periods (i.e., studying horizon of the operation problem) is used in this study. In reservoir operation, the forecast lead time H is assumed to be the same as the length of remaining operation periods (i.e., the lead time H is N periods at the beginning, N  1 periods when decision moves to next period, and so on). SOP, DP, and SDP models are then used to generate reservoir operation decisions with various synthetic streamflow forecast products.

Result analysis

The effect of streamflow forecast uncertainty on real-time reservoir operation is analyzed with reservoir operation models DP, SDP, and SOP. In the context of forecast uncertainty analysis, the effect of streamflow variability and reservoir capacity are also assessed under a pre-specified forecast uncertainty level, as shown in Table 1.

Conclusions

Streamflow forecast uncertainty plays an important role in reservoir operation, but the effects of forecast uncertainty on reservoir operation have yet to be thoroughly addressed in a unifying framework. Rather than treating the forecast products as ad hoc inputs to reservoir operation models, this study provides a method to characterize the forecast uncertainty evolution and explicitly assess the effect of streamflow forecast uncertainty on real-time reservoir operation. The Martingale Model

Acknowledgements

This research was partially supported by the China Overseas Scholarship Foundation, the National Natural Science Foundation of China (Project No. 50928901) and the US National Aeronautics and Space Administration (NASA) grant (Project No. NNX08AL94G). The authors are grateful for the numerous helpful suggestions from Dr. Mohamad Hejazi on the early versions of this paper.

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